determine the correct answers to the calculation shown below to the correct number of significant figures?
a. (32.453)(34.23+1.17)/(2.26-1.811)(0.00378)=9.671716784=9.7
b. (3.23+0.0018)=3.2318=3.2
c. (82.97-0.012)/(1.100)(21.9)=1651.618364
To determine the correct number of significant figures in a calculation, you need to consider the significant figures in each number being used. Here's how you can determine the correct answers for each calculation to the correct number of significant figures:
a. (32.453)(34.23+1.17)/(2.26-1.811)(0.00378)=9.671716784=9.7
In this calculation, you need to consider the number of significant figures in each term:
- 32.453 has 5 significant figures.
- 34.23 has 4 significant figures.
- 1.17 has 3 significant figures.
- 2.26 has 3 significant figures.
- 1.811 has 4 significant figures.
- 0.00378 has 3 significant figures.
To ensure the correct number of significant figures in the final answer, you need to use the least number of significant figures among the given numbers. In this case, it is 3 significant figures, which is the number of significant figures in 0.00378. Therefore, the correct answer is 9.7.
b. (3.23+0.0018)=3.2318=3.2
In this calculation, you only need to consider the significant figures in each term:
- 3.23 has 3 significant figures.
- 0.0018 has 2 significant figures.
Again, you should use the least number of significant figures among the given numbers, so the correct answer would be rounded to 3.2.
c. (82.97-0.012)/(1.100)(21.9)=1651.618364
In this calculation, you need to consider the significant figures in each term:
- 82.97 has 4 significant figures.
- 0.012 has 2 significant figures.
- 1.100 has 4 significant figures.
- 21.9 has 3 significant figures.
The final answer should have the same number of significant figures as the term with the least number of significant figures, which is 2 significant figures in 0.012. Therefore, the correct answer should be rounded to 1651.62.